I have found that the most common form of eponyms has been to name new diseases after the first person to be identified having suffered from it. This may not be the case with all diseases but it is with most I know.

Parkinson's and Hodgkin's come to mind.

Another form of eponyms is practiced in sport and, in particular in gymnastics where a new technique is named after the gymnast who first performs it successfully in public. There are techniques called a Katchev, a Korbut and even a Kim.